Path: utzoo!utgpu!news-server.csri.toronto.edu!cs.utexas.edu!uwm.edu!zaphod.mps.ohio-state.edu!sol.ctr.columbia.edu!bronze!chalmers From: chalmers@bronze.ucs.indiana.edu (David Chalmers) Newsgroups: comp.ai.philosophy Subject: Re: Minds, machines, and Godel Message-ID: <1991Jan18.000254.22704@bronze.ucs.indiana.edu> Date: 18 Jan 91 00:02:54 GMT References: <1991Jan17.170401.8536@bronze.ucs.indiana.edu> <1991Jan17.191340.28824@sics.se> Organization: Indiana University, Bloomington Lines: 21 In article <1991Jan17.191340.28824@sics.se> torkel@sics.se (Torkel Franzen) writes: > We have no grounds whatever for claiming that we can see the Godel sentence >of the system to be true. So you must claim either (a) we cannot see the Godel sentence of Principia Mathematica to be true, or (b) there are some relevant differences between the general Turing Machine case and Principia Mathematica. I don't see any grounds for claiming (a) -- Godel would deny it and so would I. The Godel sentence for Principia Mathematica seems as well supported as most statements of mathematics. If you claim (b), I would like to see the relevant differences spelled out. (N.B. Any Turing Machine system for judging the truth of statements of arithmetic can straightforwardly be turned into a first-order axiomatic system for generating such statements.) -- Dave Chalmers (dave@cogsci.indiana.edu) Center for Research on Concepts and Cognition, Indiana University. "It is not the least charm of a theory that it is refutable."